TY - GEN A1 - Aguado, Felicidad A1 - Cabalar, Pedro A1 - Fandinno, Jorge A1 - Pearce, David A1 - Perez, Gilberto A1 - Vidal, Concepcion T1 - Revisiting explicit negation in answer set programming T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson's strong negation. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1104 KW - Answer Set Programming KW - non-monotonic reasoning KW - Equilibrium logic KW - explicit negation Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-469697 SN - 1866-8372 IS - 1104 SP - 908 EP - 924 ER - TY - JOUR A1 - Aguado, Felicidad A1 - Cabalar, Pedro A1 - Fandinno, Jorge A1 - Pearce, David A1 - Perez, Gilberto A1 - Vidal, Concepcion T1 - Forgetting auxiliary atoms in forks JF - Artificial intelligence N2 - In this work we tackle the problem of checking strong equivalence of logic programs that may contain local auxiliary atoms, to be removed from their stable models and to be forbidden in any external context. We call this property projective strong equivalence (PSE). It has been recently proved that not any logic program containing auxiliary atoms can be reformulated, under PSE, as another logic program or formula without them – this is known as strongly persistent forgetting. In this paper, we introduce a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There, in which we deal with a new connective ‘|’ we call fork. We provide a semantic characterisation of PSE for forks and use it to show that, in this extension, it is always possible to forget auxiliary atoms under strong persistence. We further define when the obtained fork is representable as a regular formula. KW - Answer set programming KW - Non-monotonic reasoning KW - Equilibrium logic KW - Denotational semantics KW - Forgetting KW - Strong equivalence Y1 - 2019 U6 - https://doi.org/10.1016/j.artint.2019.07.005 SN - 0004-3702 SN - 1872-7921 VL - 275 SP - 575 EP - 601 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Aguado, Felicidad A1 - Cabalar, Pedro A1 - Fandiño, Jorge A1 - Pearce, David A1 - Perez, Gilberto A1 - Vidal-Peracho, Concepcion T1 - Revisiting Explicit Negation in Answer Set Programming JF - Theory and practice of logic programming KW - Answer set programming KW - Non-monotonic reasoning KW - Equilibrium logic KW - Explicit negation Y1 - 2019 U6 - https://doi.org/10.1017/S1471068419000267 SN - 1471-0684 SN - 1475-3081 VL - 19 IS - 5-6 SP - 908 EP - 924 PB - Cambridge Univ. Press CY - New York ER - TY - GEN A1 - Bosser, Anne-Gwenn A1 - Cabalar, Pedro A1 - Dieguez, Martin A1 - Schaub, Torsten H. T1 - Introducing temporal stable models for linear dynamic logic T2 - 16th International Conference on Principles of Knowledge Representation and Reasoning N2 - We propose a new temporal extension of the logic of Here-and-There (HT) and its equilibria obtained by combining it with dynamic logic over (linear) traces. Unlike previous temporal extensions of HT based on linear temporal logic, the dynamic logic features allow us to reason about the composition of actions. For instance, this can be used to exercise fine grained control when planning in robotics, as exemplified by GOLOG. In this paper, we lay the foundations of our approach, and refer to it as Linear Dynamic Equilibrium Logic, or simply DEL. We start by developing the formal framework of DEL and provide relevant characteristic results. Among them, we elaborate upon the relationships to traditional linear dynamic logic and previous temporal extensions of HT. Y1 - 2018 UR - https://www.dc.fi.udc.es/~cabalar/del.pdf SP - 12 EP - 21 PB - ASSOC Association for the Advancement of Artificial Intelligence CY - Palo Alto ER - TY - CHAP A1 - Cabalar, Pedro T1 - Existential quantifiers in the rule body N2 - In this paper we consider a simple syntactic extension of Answer Set Programming (ASP) for dealing with (nested) existential quantifiers and double negation in the rule bodies, in a close way to the recent proposal RASPL-1. The semantics for this extension just resorts to Equilibrium Logic (or, equivalently, to the General Theory of Stable Models), which provides a logic-programming interpretation for any arbitrary theory in the syntax of Predicate Calculus. We present a translation of this syntactic class into standard logic programs with variables (either disjunctive or normal, depending on the input rule heads), as those allowed by current ASP solvers. The translation relies on the introduction of auxiliary predicates and the main result shows that it preserves strong equivalence modulo the original signature. Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-41476 ER - TY - JOUR A1 - Cabalar, Pedro A1 - Dieguez, Martin A1 - Schaub, Torsten H. A1 - Schuhmann, Anna T1 - Towards metric temporal answer set programming JF - Theory and practice of logic programming N2 - We elaborate upon the theoretical foundations of a metric temporal extension of Answer Set Programming. In analogy to previous extensions of ASP with constructs from Linear Temporal and Dynamic Logic, we accomplish this in the setting of the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic. More precisely, we develop our logic on the same semantic underpinnings as its predecessors and thus use a simple time domain of bounded time steps. This allows us to compare all variants in a uniform framework and ultimately combine them in a common implementation. Y1 - 2020 U6 - https://doi.org/10.1017/S1471068420000307 SN - 1471-0684 SN - 1475-3081 VL - 20 IS - 5 SP - 783 EP - 798 PB - Cambridge Univ. Press CY - Cambridge [u.a.] ER - TY - JOUR A1 - Cabalar, Pedro A1 - Fandinno, Jorge A1 - Garea, Javier A1 - Romero, Javier A1 - Schaub, Torsten H. T1 - Eclingo BT - a solver for epistemic logic programs JF - Theory and practice of logic programming N2 - We describe eclingo, a solver for epistemic logic programs under Gelfond 1991 semantics built upon the Answer Set Programming system clingo. The input language of eclingo uses the syntax extension capabilities of clingo to define subjective literals that, as usual in epistemic logic programs, allow for checking the truth of a regular literal in all or in some of the answer sets of a program. The eclingo solving process follows a guess and check strategy. It first generates potential truth values for subjective literals and, in a second step, it checks the obtained result with respect to the cautious and brave consequences of the program. This process is implemented using the multi-shot functionalities of clingo. We have also implemented some optimisations, aiming at reducing the search space and, therefore, increasing eclingo 's efficiency in some scenarios. Finally, we compare the efficiency of eclingo with two state-of-the-art solvers for epistemic logic programs on a pair of benchmark scenarios and show that eclingo generally outperforms their obtained results. KW - Answer Set Programming KW - Epistemic Logic Programs KW - Non-Monotonic KW - Reasoning KW - Conformant Planning Y1 - 2020 U6 - https://doi.org/10.1017/S1471068420000228 SN - 1471-0684 SN - 1475-3081 VL - 20 IS - 6 SP - 834 EP - 847 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Cabalar, Pedro A1 - Fandinno, Jorge A1 - Lierler, Yuliya T1 - Modular Answer Set Programming as a formal specification language JF - Theory and practice of logic programming N2 - In this paper, we study the problem of formal verification for Answer Set Programming (ASP), namely, obtaining aformal proofshowing that the answer sets of a given (non-ground) logic programPcorrectly correspond to the solutions to the problem encoded byP, regardless of the problem instance. To this aim, we use a formal specification language based on ASP modules, so that each module can be proved to capture some informal aspect of the problem in an isolated way. This specification language relies on a novel definition of (possibly nested, first order)program modulesthat may incorporate local hidden atoms at different levels. Then,verifyingthe logic programPamounts to prove some kind of equivalence betweenPand its modular specification. KW - Answer Set Programming KW - formal specification KW - formal verification KW - modular logic programs Y1 - 2020 U6 - https://doi.org/10.1017/S1471068420000265 SN - 1471-0684 SN - 1475-3081 VL - 20 IS - 5 SP - 767 EP - 782 PB - Cambridge University Press CY - New York ER - TY - JOUR A1 - Cabalar, Pedro A1 - Fandinno, Jorge A1 - Schaub, Torsten H. A1 - Schellhorn, Sebastian T1 - Gelfond-Zhang aggregates as propositional formulas JF - Artificial intelligence N2 - Answer Set Programming (ASP) has become a popular and widespread paradigm for practical Knowledge Representation thanks to its expressiveness and the available enhancements of its input language. One of such enhancements is the use of aggregates, for which different semantic proposals have been made. In this paper, we show that any ASP aggregate interpreted under Gelfond and Zhang's (GZ) semantics can be replaced (under strong equivalence) by a propositional formula. Restricted to the original GZ syntax, the resulting formula is reducible to a disjunction of conjunctions of literals but the formulation is still applicable even when the syntax is extended to allow for arbitrary formulas (including nested aggregates) in the condition. Once GZ-aggregates are represented as formulas, we establish a formal comparison (in terms of the logic of Here-and-There) to Ferraris' (F) aggregates, which are defined by a different formula translation involving nested implications. In particular, we prove that if we replace an F-aggregate by a GZ-aggregate in a rule head, we do not lose answer sets (although more can be gained). This extends the previously known result that the opposite happens in rule bodies, i.e., replacing a GZ-aggregate by an F-aggregate in the body may yield more answer sets. Finally, we characterize a class of aggregates for which GZ- and F-semantics coincide. KW - Aggregates KW - Answer Set Programming Y1 - 2019 U6 - https://doi.org/10.1016/j.artint.2018.10.007 SN - 0004-3702 SN - 1872-7921 VL - 274 SP - 26 EP - 43 PB - Elsevier CY - Amsterdam ER - TY - GEN A1 - Cabalar, Pedro A1 - Fandinno, Jorge A1 - Schaub, Torsten H. A1 - Schellhorn, Sebastian T1 - Lower Bound Founded Logic of Here-and-There T2 - Logics in Artificial Intelligence N2 - A distinguishing feature of Answer Set Programming is that all atoms belonging to a stable model must be founded. That is, an atom must not only be true but provably true. This can be made precise by means of the constructive logic of Here-and-There, whose equilibrium models correspond to stable models. One way of looking at foundedness is to regard Boolean truth values as ordered by letting true be greater than false. Then, each Boolean variable takes the smallest truth value that can be proven for it. This idea was generalized by Aziz to ordered domains and applied to constraint satisfaction problems. As before, the idea is that a, say integer, variable gets only assigned to the smallest integer that can be justified. In this paper, we present a logical reconstruction of Aziz’ idea in the setting of the logic of Here-and-There. More precisely, we start by defining the logic of Here-and-There with lower bound founded variables along with its equilibrium models and elaborate upon its formal properties. Finally, we compare our approach with related ones and sketch future work. Y1 - 2019 SN - 978-3-030-19570-0 SN - 978-3-030-19569-4 U6 - https://doi.org/10.1007/978-3-030-19570-0_34 SN - 0302-9743 SN - 1611-3349 VL - 11468 SP - 509 EP - 525 PB - Springer CY - Cham ER - TY - JOUR A1 - Cabalar, Pedro A1 - Kaminski, Roland A1 - Schaub, Torsten H. A1 - Schuhmann, Anna T1 - Temporal answer set programming on finite traces JF - Theory and practice of logic programming N2 - In this paper, we introduce an alternative approach to Temporal Answer Set Programming that relies on a variation of Temporal Equilibrium Logic (TEL) for finite traces. This approach allows us to even out the expressiveness of TEL over infinite traces with the computational capacity of (incremental) Answer Set Programming (ASP). Also, we argue that finite traces are more natural when reasoning about action and change. As a result, our approach is readily implementable via multi-shot ASP systems and benefits from an extension of ASP's full-fledged input language with temporal operators. This includes future as well as past operators whose combination offers a rich temporal modeling language. For computation, we identify the class of temporal logic programs and prove that it constitutes a normal form for our approach. Finally, we outline two implementations, a generic one and an extension of the ASP system clingo. Under consideration for publication in Theory and Practice of Logic Programming (TPLP) Y1 - 2018 U6 - https://doi.org/10.1017/S1471068418000297 SN - 1471-0684 SN - 1475-3081 VL - 18 IS - 3-4 SP - 406 EP - 420 PB - Cambridge Univ. Press CY - New York ER -